Representations and identities of plactic-like monoids

Finite rank plactic monoids are infinite monoids arising from a natural combinatorial multiplication (determined by Schensted’s insertion algorithm) on semistandard tableaux over a fixed finite alphabet. Each finite rank plactic monoid can be faithfully represented by matrices over the tropical semiring; the existence of such representations implies that these monoids satisfy non-trivial semigroup identities (joint work Kambites).

There are several well-studied families of finite rank 'plactic-like' monoids whose elements are combinatorial gadgets of a particular type over a fixed finite alphabet, and whose multiplication can be defined by means of an insertion algorithm. It turns out that for most of these well-studied families the finite rank plactic-like monoids can be faithfully represented by matrices over semirings from a large class (including the tropical semiring). Using our representations, we prove some results about the variety generated by a single finite rank plactic-like monoid (joint work with Cain, Kambites, and Malheiro).

Date and Venue

Start Date
Venue
Online Zoom meeting
End Date

Speaker

Marianne Johnson

Speaker's Institution

University of Manchester

Files

Area

Semigroups, Automata and Languages

Financiamento